Mechanical analysis method for reinforced component based on orthotropic thin plate theory

Abstract

This invention provides a mechanical analysis method for reinforced steel components based on orthotropic thin plate theory. It selects the cross-shaped model of the welded reinforced steel component as the smallest computational unit, equating it to orthotropic thin plate elements with uniform planar dimensions, and determines the equivalent thickness of the thin plate according to the construction of the steel cross nodes. Based on the principle of stiffness equivalence, the equivalent material mechanical parameters of the thin plate are calculated. These parameters are substituted into classical thin plate theory to construct a reduced stiffness matrix. Through thickness integration, in-plane and out-of-plane stiffness matrices are obtained. Then, a generalized force-deformation constitutive model is built based on these two types of stiffness matrices. Actual working condition loads are applied to complete the mechanical response analysis of the reinforced steel component, outputting displacement and stress distribution data. The results can directly guide the hoisting construction, alignment connection, and structural alignment control of the reinforced steel component. This solves the problems of complex deformation calculation and large workload for welded reinforced steel components.

Description

Technical Field

[0001] This invention relates to the field of concrete structure engineering technology, and in particular to a mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory. Background Technology

[0002] Reinforcing steel components can be formed by binding or welding. Binded reinforcing steel components have low stiffness and are prone to changes in spacing during transportation and hoisting. Furthermore, they are more difficult to automate than welded components. Therefore, most reinforcing steel components are formed using welding. Welded reinforcing steel components are prefabricated in sections in the factory and transported to the construction site for installation. This requires multiple hoisting operations, and the longitudinal reinforcement of upper and lower sections needs to be connected using methods such as conical sleeves during installation. The overall stiffness of the reinforcing steel components directly affects hoisting safety and the ease of alignment. In addition, when the structure is irregularly shaped, such as with a certain angle of inclination, the overall stiffness of the reinforcing steel components will also directly affect the structural alignment and the thickness of the protective layer. Therefore, deformation calculations for welded reinforcing steel components are particularly important.

[0003] Currently, when calculating the deformation of welded steel reinforcement components, rigid connections are typically used at the steel reinforcement intersections. However, weld joints are not actually rigid structures; under stress, the longitudinal and transverse reinforcements rotate relative to each other. Therefore, weld joints are essentially semi-rigid structures. Traditional rigid connection methods will severely underestimate the deformation of welded steel reinforcement components, leading to problems such as excessive hoisting deformation, difficulties in connecting longitudinal reinforcements, structural alignment not meeting design requirements, and substandard protective layer thickness. If the actual stiffness of the steel reinforcement intersections is considered, the workload of calculating steel reinforcement connections is substantial due to the numerous weld joint locations. Furthermore, most steel reinforcement components are irregular structures with complex weld joint distributions, making the calculation workload even more enormous. Summary of the Invention

[0004] The main objective of this invention is to provide a mechanical analysis method for steel reinforcement components based on orthotropic thin plate theory, thereby solving the problems of complex deformation calculation and large workload in welded steel reinforcement components.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory, the method comprising: S1. Select the cross-shaped model of the welded steel reinforcement components as the smallest basic calculation unit. Equip this basic calculation unit with the structural size matching principle as an orthogonal anisotropic thin plate element with consistent planar size, and determine the equivalent thickness of the thin plate based on the structural characteristics of the steel reinforcement intersection node. S2. Based on the principle of equivalent structural stiffness, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate are obtained by equivalent conversion of the stress and deformation of the steel reinforcement element and the thin plate element. S3. Substitute the obtained equivalent material mechanical parameters into the classical thin plate theory system to construct the reduced stiffness matrix of the equivalent thin plate. S4. Using the reduced stiffness matrix as the basis for calculation, the equivalent thickness of the thin plate is integrated to derive the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate. S5. Based on the in-plane stiffness matrix and out-of-plane stiffness matrix, construct a generalized force-deformation constitutive model of anisotropic thin plate, apply external loads of the actual working conditions of the steel reinforcement components to the model, complete the overall mechanical response analysis of the steel reinforcement components, and obtain the stress and deformation results.

[0006] In the preferred embodiment, in step S1, when determining the equivalent thickness of the orthogonal anisotropic thin plate unit, the longitudinal and transverse bars at the cross intersection of the reinforcing steel components are used as the calculation basis. The diameters of the longitudinal and transverse bars at the intersection are directly added together, and the resulting value is used as the equivalent thickness of the thin plate unit, ensuring that the structural thickness characteristics of the equivalent thin plate and the original reinforcing steel cross unit are completely matched.

[0007] In the preferred embodiment, in step S2, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate obtained by solving specifically include the in-plane shear modulus used to characterize the in-plane shear stress characteristics of the thin plate, and the out-of-plane rotation modulus used to characterize the out-of-plane rotation stress characteristics of the thin plate. The two types of parameters together accurately reflect the true mechanical properties of the semi-rigid weld joints of the reinforcing steel components.

[0008] In the preferred embodiment, in step S2, when solving for the equivalent material mechanical parameters, fixed consolidation constraints are applied to the ends of the longitudinal or transverse reinforcement of the basic calculation unit of the steel reinforcement component. In-plane forces and out-of-plane bending moment loads are applied to the unit respectively. The total deformation of the steel reinforcement is decomposed into three components: the bending deformation of the steel reinforcement itself, the rotational deformation of the steel reinforcement relative to the intersection node, and the deformation caused by the bending of the associated steel reinforcement. The actual deformation of the steel reinforcement unit is converted into the equivalent deformation of the thin plate unit through the deformation equivalence principle, and the equivalent material mechanical parameters of the thin plate are calculated in reverse.

[0009] In the preferred scheme, in step S3, when establishing the equivalent thin plate reduced stiffness matrix, the in-plane shear modulus and out-of-plane rotation modulus obtained by solving are combined with the lateral deformation ratio parameters of the longitudinal and transverse reinforcing bars of the steel reinforcement component under stress. The reduced stiffness matrix is ​​constructed according to the mechanical theory of orthotropic thin plates to realize the unified correlation between the material parameters and stiffness characteristics of the equivalent thin plate.

[0010] In the preferred embodiment, in step S4, when calculating the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate, the in-plane stiffness matrix is ​​obtained by multiplying the reduced stiffness matrix with the equivalent thickness of the thin plate, and the out-of-plane stiffness matrix is ​​obtained by proportionally multiplying the reduced stiffness matrix with the cube of the equivalent thickness of the thin plate. The two types of stiffness matrices correspond to the in-plane stress and out-of-plane bending stress characteristics of the reinforcing steel components, respectively.

[0011] In the preferred embodiment, after completing the mechanical response analysis of the reinforcing steel components in step S5, the overall displacement distribution data and internal stress distribution data of the reinforcing steel components under external loads are output. The obtained data can be directly used to guide the hoisting construction, alignment connection and structural alignment control of the reinforcing steel components.

[0012] In the preferred embodiment, in step S2, when solving for the equivalent material mechanical parameters, the in-plane rotational stiffness and out-of-plane rotational stiffness of the weld point are dynamically corrected by combining the specifications and dimensions of the longitudinal and transverse reinforcing bars of the steel reinforcement component, the actual welding process parameters, and the weld leg size. Based on the corrected weld point rotational stiffness, the equivalent material mechanical parameters of the thin plate are calculated.

[0013] In the preferred scheme, in step S1, for irregular steel reinforcement components with irregular shapes and non-uniform steel reinforcement mesh, an adaptive mesh generation method is used to generate non-standard cross-shaped basic calculation units. The equivalent parameters and stiffness matrix of the thin plate are corrected for the non-standard units through the principle of local stiffness equivalence. Then, the local equivalent results are spliced ​​and integrated to complete the mechanical analysis of the overall irregular steel reinforcement component.

[0014] In the preferred embodiment, in step S1, for complex steel reinforcement components with double or multiple layers, the layered thin plate equivalent method is adopted to convert each layer of steel reinforcement into an independent orthogonal anisotropic thin plate element. In steps S3 to S4, the reduced stiffness matrix, in-plane stiffness matrix and out-of-plane stiffness matrix of each layer of thin plate are calculated respectively. The stiffness matrices of each layer are superimposed and merged to form an overall equivalent model. Then, based on the overall model, step S5 is executed to complete the mechanical response analysis.

[0015] This invention provides a mechanical analysis method for reinforced steel components based on orthotropic thin plate theory. By simplifying welded reinforced steel components into a thin-plate structure through orthotropic thin-plate theory, this method effectively solves the problems of large deformation prediction deviations and massive computational workload inherent in traditional calculation methods. It accurately reflects the true stress and deformation characteristics of welded reinforced steel components. This method abandons the traditional rigid connection assumption, fully considering the semi-rigid mechanical characteristics of weld joints. Through the deformation equivalence principle, it restores the true stress state of the steel reinforcement intersection, significantly improving the accuracy of deformation calculations. This effectively avoids problems such as excessive hoisting deformation, difficulty in longitudinal reinforcement alignment, structural alignment deviations, and unqualified protective layer thickness caused by insufficient deformation estimation.

[0016] This invention simplifies the complex steel mesh structure into a standard thin plate element. Based on stiffness equivalence and classical thin plate theory, it completes the stiffness matrix construction and mechanical response solution. It eliminates the need for detailed modeling of a large number of weld points, significantly reducing the workload and time cost of computation. It enables rapid and efficient analysis of the mechanical behavior of steel reinforcement components and can meet the actual needs of rapid calculation and analysis in engineering sites.

[0017] Meanwhile, this method is applicable to welded steel reinforcement components with various structural forms. It is not only suitable for steel reinforcement components with conventional regular grids, but also for irregular steel reinforcement components with irregular shapes and non-uniform arrangements. It can also perform mechanical calculations on complex steel reinforcement components with double and multi-layer reinforcement, which greatly expands the scope of application of mechanical analysis methods for steel reinforcement components.

[0018] The mechanical analysis results output by this invention can be directly used to guide the factory prefabrication, transportation, hoisting, and on-site installation of steel reinforcement components. It provides reliable theoretical support for the safety management and quality assurance of steel reinforcement components, effectively improves the efficiency and quality of steel reinforcement component construction, and promotes the efficient implementation of steel reinforcement component prefabrication and installation technology in concrete structure engineering. Attached Figure Description

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the method for calculating the equivalent stiffness of steel reinforcement components based on thin plate theory according to the present invention. Figure 2 It is the basic unit of theoretical analysis in this invention; Figure 3 This invention provides a calculation model for solving the mechanical parameters of an equivalent thin plate. Detailed Implementation

[0020] Example 1 like Figure 1-3 As shown, a mechanical analysis method for reinforced steel components based on orthotropic thin plate theory is presented. This method includes: S1. Select the cross-shaped model of the welded steel reinforcement components as the smallest basic calculation unit. Equip this basic calculation unit with the structural size matching principle as an orthogonal anisotropic thin plate element with consistent planar size, and determine the equivalent thickness of the thin plate based on the structural characteristics of the steel reinforcement intersection node. S2. Based on the principle of equivalent structural stiffness, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate are obtained by equivalent conversion of the stress and deformation of the steel reinforcement element and the thin plate element. S3. Substitute the obtained equivalent material mechanical parameters into the classical thin plate theory system to construct the reduced stiffness matrix of the equivalent thin plate. S4. Using the reduced stiffness matrix as the basis for calculation, the equivalent thickness of the thin plate is integrated to derive the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate. S5. Based on the in-plane stiffness matrix and out-of-plane stiffness matrix, construct a generalized force-deformation constitutive model of anisotropic thin plate, apply external loads of the actual working conditions of the steel reinforcement components to the model, complete the overall mechanical response analysis of the steel reinforcement components, and obtain the stress and deformation results.

[0021] This application addresses the industry pain points of welded steel reinforcement components, such as the semi-rigid structure of weld joints, the significant underestimation of deformation by traditional rigid assumptions, and the enormous computational burden of detailed modeling for fully semi-rigid components. It employs the stiffness equivalence principle and classical orthotropic thin plate theory as core theoretical support, equating the discrete steel reinforcement mesh structure to a continuous, homogeneous, orthotropic thin plate component. Using the minimum stress element at the cross intersection of steel reinforcements as the equivalent benchmark, the semi-rigid mechanical properties of the weld joints are restored through deformation decomposition. In-plane and out-of-plane stiffness matrices are constructed based on the thin plate stiffness integral formula, and a global mechanical model is established based on the generalized force-deformation constitutive relationship of elasticity. This method can accurately solve the deformation and stress distribution of steel reinforcement components without modeling a massive number of weld joints individually. This approach simplifies the complex spatial steel reinforcement structure into a two-dimensional thin plate mechanics problem, reducing computational costs while maintaining computational accuracy. It balances the accuracy and efficiency of mechanical analysis of welded steel reinforcement components, adapting to the practical needs of rapid analysis in engineering sites.

[0022] In the preferred embodiment, in step S1, when determining the equivalent thickness of the orthogonal anisotropic thin plate unit, the longitudinal and transverse bars at the cross intersection of the reinforcing steel components are used as the calculation basis. The diameters of the longitudinal and transverse bars at the intersection are directly added together, and the resulting value is used as the equivalent thickness of the thin plate unit, ensuring that the structural thickness characteristics of the equivalent thin plate and the original reinforcing steel cross unit are completely matched.

[0023] The core load-bearing unit of the welded steel reinforcement component is the cross-shaped structure of longitudinal and transverse reinforcement. This unit is the smallest repeating structural unit of the component, and its planar geometric dimensions are perfectly matched to be equivalent to a thin plate unit. The equivalent thickness is the sum of the diameters of the longitudinal and transverse reinforcements at the intersection point. ,like Figure 2 As shown, the geometric characteristics of discrete steel reinforcement elements and continuous thin plate elements are unified, providing basic geometric conditions for subsequent stiffness equivalence calculations.

[0024] In the preferred embodiment, in step S2, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate obtained by solving specifically include the in-plane shear modulus used to characterize the in-plane shear stress characteristics of the thin plate, and the out-of-plane rotation modulus used to characterize the out-of-plane rotation stress characteristics of the thin plate. The two types of parameters together accurately reflect the true mechanical properties of the semi-rigid weld joints of the reinforcing steel components.

[0025] In the preferred embodiment, in step S2, when solving for the equivalent material mechanical parameters, fixed consolidation constraints are applied to the ends of the longitudinal or transverse reinforcement of the basic calculation unit of the steel reinforcement component. In-plane forces and out-of-plane bending moment loads are applied to the unit respectively. The total deformation of the steel reinforcement is decomposed into three components: the bending deformation of the steel reinforcement itself, the rotational deformation of the steel reinforcement relative to the intersection node, and the deformation caused by the bending of the associated steel reinforcement. The actual deformation of the steel reinforcement unit is converted into the equivalent deformation of the thin plate unit through the deformation equivalence principle, and the equivalent material mechanical parameters of the thin plate are calculated in reverse.

[0026] The equivalent sheet metal mechanical parameters include the in-plane shear modulus of the sheet metal. , out-of-plane rotational modulus of a thin plate , .

[0027] Theoretical models for solving in-plane shear modulus and out-of-plane rotational modulus are as follows: Figure 3 As shown.

[0028] To solve for the in-plane shear modulus, consolidation constraints are applied to both ends of the longitudinal reinforcement, and in-plane forces are applied to the ends of the transverse reinforcement. The shear deformation of the transverse ribs is obtained. for:

[0029] In the formula: This refers to the shear deformation of the transverse reinforcement caused by bending of the transverse reinforcement itself. This refers to the shear deformation of the transverse reinforcement caused by its in-plane rotation relative to the longitudinal reinforcement. Shear deformation of transverse reinforcement caused by bending of longitudinal reinforcement; The free length of the transverse stiffener in the basic unit. The free length of the longitudinal reinforcement in the basic unit. The elastic modulus of the steel reinforcement. , The moments of inertia of the longitudinal and transverse reinforcement sections are respectively. It represents the rotational stiffness of the transverse reinforcement relative to the longitudinal reinforcement in the plane.

[0030] The force required to apply to a thin plate under the same deformation :

[0031]

[0032]

[0033] In the formula: For thin plate shear stress, This represents the shear area of ​​the thin plate along the longitudinal stiffener direction. This refers to the in-plane shear modulus of the thin plate. The thickness is the thickness of the sheet.

[0034] Depend on The in-plane shear stiffness of the thin plate can be obtained. :

[0035] Following the same derivation method, the in-plane shear modulus of the thin plate under the condition of constrained longitudinal ribs is obtained. :

[0036] To solve for the out-of-plane rotation modulus, fixed constraints are applied to both ends of the longitudinal reinforcement, and out-of-plane bending moments with the longitudinal reinforcement as the axis of rotation are applied to the ends of the transverse reinforcement. Outer corner of the end face of the transverse reinforcement for:

[0037]

[0038]

[0039]

[0040] In the formula: The angle at the end of the horizontal reinforcement caused by the bending of the horizontal reinforcement itself; The angle at the end of the transverse reinforcement caused by the rotation of the longitudinal reinforcement as the axis of rotation; The angle at the end of the transverse reinforcement caused by the rotation of the longitudinal reinforcement; The rotational stiffness of the transverse reinforcement with the longitudinal reinforcement as the axis of rotation; This refers to the torsional modulus of the reinforcing steel. Let be the torsional moment of inertia of the cross section of the transverse reinforcement.

[0041] Out-of-plane bending moment required for thin plates under the same deformation for:

[0042] Depend on The out-of-plane rotational stiffness of the thin plate about the longitudinal stiffener direction can be obtained. :

[0043] In the formula: This indicates the proportion of lateral deformation in the direction of the longitudinal reinforcement when the transverse reinforcement is subjected to force. This indicates the proportion of lateral deformation in the direction of the transverse reinforcement when the longitudinal reinforcement is subjected to force.

[0044] Following the same derivation method, the out-of-plane rotational stiffness of the thin plate about the direction of the transverse stiffener is obtained. :

[0045] In the formula: The rotational stiffness of the longitudinal reinforcement with the transverse reinforcement as the axis of rotation; Let be the torsional moment of inertia of the longitudinal reinforcement section.

[0046] In the preferred scheme, in step S3, when establishing the equivalent thin plate reduced stiffness matrix, the in-plane shear modulus and out-of-plane rotation modulus obtained by solving are combined with the lateral deformation ratio parameters of the longitudinal and transverse reinforcing bars of the steel reinforcement component under stress. The reduced stiffness matrix is ​​constructed according to the mechanical theory of orthotropic thin plates to realize the unified correlation between the material parameters and stiffness characteristics of the equivalent thin plate.

[0047] Reduced stiffness matrix The calculation is as follows:

[0048]

[0049] In the formula, , These represent the axial stiffness of the transverse and longitudinal reinforcement bars, respectively. Represents the deformation coupling stiffness of the longitudinal and transverse ribs. The in-plane shear stiffness represents the semi-rigidity of the weld joint. , Represents the coupling stiffness between axial force and shear force; This represents the proportion of transverse deformation in the direction of the longitudinal reinforcement when the transverse reinforcement is subjected to force. When the longitudinal reinforcement is subjected to force, the transverse deformation ratio in the transverse reinforcement direction is the same as that in the longitudinal reinforcement direction. The two are the cross Poisson ratios of orthotropic materials, used to describe the deformation coupling relationship between two perpendicular directions of an equivalent thin plate.

[0050] In the formula, the subscript 1 represents the direction of the transverse reinforcement of the steel reinforcement component; the subscript 2 represents the direction of the longitudinal reinforcement of the steel reinforcement component; and the subscript 6 represents the in-plane shear direction at the intersection of the longitudinal and transverse reinforcement. This definition is followed in subsequent calculations.

[0051] In the preferred embodiment, in step S4, when calculating the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate, the in-plane stiffness matrix is ​​obtained by multiplying the reduced stiffness matrix with the equivalent thickness of the thin plate, and the out-of-plane stiffness matrix is ​​obtained by proportionally multiplying the reduced stiffness matrix with the cube of the equivalent thickness of the thin plate. The two types of stiffness matrices correspond to the in-plane stress and out-of-plane bending stress characteristics of the reinforcing steel components, respectively.

[0052] The in-plane stiffness matrix out-of-plane stiffness matrix The calculation is as follows:

[0053]

[0054]

[0055]

[0056] In the formula, The in-plane axial stiffness in the direction of the transverse reinforcement. This refers to the in-plane axial stiffness in the direction of the longitudinal reinforcement. For the in-plane coupling stiffness of the longitudinal and transverse ribs, In-plane shear stiffness characterizes the ability of the longitudinal-transverse reinforcement intersection weld joint to resist relative in-plane slippage. , It is an in-plane axial-shear coupling stiffness that corrects the interaction between bending and torsional deformation. It is the overall structural stiffness of the steel reinforcement component under in-plane stress, which is determined by... Multiply by equivalent thickness This yields the tensile, compressive, and shear forces within the plane of the corresponding steel reinforcement component.

[0057] The out-of-plane bending stiffness is in the direction of the transverse reinforcement. This refers to the out-of-plane bending stiffness in the longitudinal reinforcement direction. For the out-of-plane bending-torsional coupling stiffness of the longitudinal and transverse reinforcements, Out-of-plane torsional stiffness characterizes the overall resistance of a steel reinforcement component to torsion. , For out-of-plane bending-torsional coupling stiffness, the interaction between bending deformation and torsional deformation is corrected.

[0058] It is the material stiffness basis that determines the inherent stiffness properties of the equivalent material of the steel reinforcement component; It is the overall structural stiffness of the steel reinforcement component under in-plane stress, corresponding to the tensile, compressive, and shear stresses in the plane of the steel reinforcement component, determining the deformation resistance of the steel reinforcement component in the plane, and directly related to the shear characteristics of the weld point; It is the overall structural stiffness of the reinforcing steel component under out-of-plane stress, corresponding to the bending and torsional stresses outside the plane of the reinforcing steel component, determining the hoisting deflection and torsional control capability of the reinforcing steel component, and directly related to the bending characteristics of the reinforcing steel. The three are correlated through thickness integral, covering the full stress forms of the welded reinforcing steel component under tension, compression, shear, bending and torsion, accurately reproducing the semi-rigid mechanical behavior of the weld point.

[0059] In the preferred embodiment, after completing the mechanical response analysis of the reinforcing steel components in step S5, the overall displacement distribution data and internal stress distribution data of the reinforcing steel components under external loads are output. The obtained data can be directly used to guide the hoisting construction, alignment connection and structural alignment control of the reinforcing steel components.

[0060] The generalized force-deformation constitutive model of anisotropic thin plates is as follows:

[0061]

[0062]

[0063]

[0064] In the formula: , , These represent the axial force along the transverse reinforcement direction, the axial force along the longitudinal reinforcement direction, and the in-plane shear force, respectively. , , These represent the bending moment about the transverse reinforcement, the bending moment about the longitudinal reinforcement, and the torque, respectively. , , These represent the strain in the direction of the transverse reinforcement, the strain in the direction of the longitudinal reinforcement, and the in-plane shear strain, respectively. , , These represent the curvature in the transverse direction, the curvature in the longitudinal direction, and the out-of-plane twist, respectively.

[0065] Example 2 To further illustrate with reference to Example 1, in step S2, when solving for the equivalent material mechanical parameters, the in-plane rotational stiffness and out-of-plane rotational stiffness of the weld point are dynamically corrected by combining the specifications and dimensions of the longitudinal and transverse reinforcing bars of the steel reinforcement component, the actual welding process parameters, and the weld leg dimensions. Based on the corrected weld point rotational stiffness, the equivalent material mechanical parameters of the thin plate are calculated.

[0066] Weld joint rotational stiffness is a core indicator affecting the accuracy of the equivalent parameters of reinforcing steel components. Its value varies significantly with the steel bar specifications, welding process, and weld leg size. The fixed rotational stiffness value in the method of Example 1 cannot match the actual mechanical properties of weld joints under different engineering conditions, leading to a deviation between the equivalent parameters and the actual stress. In this embodiment, the dynamic correction theory of weld joint stiffness is introduced in the equivalent parameter solution stage of the method of Example 1. A correction formula is established by combining the actual dimensions of the reinforcing steel bar and the welding structure parameters, so that the rotational stiffness value fits the actual engineering situation, thereby improving the accuracy of the equivalent parameters and mechanical analysis from the source.

[0067] The calculation for the correction of the rotational stiffness of the weld point is as follows:

[0068]

[0069]

[0070]

[0071]

[0072] In the formula, , , To correct the in-plane rotational stiffness, out-of-plane rotational stiffness around the longitudinal ribs, and out-of-plane rotational stiffness around the transverse ribs of the weld joint; , , This refers to the initial rotational stiffness of the weld joint in Example 1; , For in-plane and out-of-plane rotational stiffness correction coefficients; , , , This is a welding process correction factor, with a fixed value determined based on welding methods such as arc welding and resistance welding. , This is a correction factor for the steel reinforcement material, determined based on steel reinforcement grades such as HRB400 and HRB500. This refers to the actual nominal diameter of the reinforcing bar. The reference steel bar diameter; The actual weld leg size, i.e., the equivalent thickness in Example 1, is the sum of the diameters of the longitudinal and transverse ribs at the intersection. This is the reference solder joint size.

[0073] This embodiment follows the core process of thin plate equivalent in embodiment 1, only adding a stiffness correction step in the equivalent parameter calculation stage. After the corrected rotational stiffness is substituted into the original calculation model, the systematic error caused by the fixed stiffness value can be effectively eliminated, so that the deformation and stress calculation results of the steel reinforcement components are highly consistent with the actual engineering state, and the reliability and engineering applicability of the mechanical analysis results are greatly improved.

[0074] Example 3 To further illustrate with reference to Example 1, in step S1, for irregular steel reinforcement components with irregular shapes and non-uniform steel reinforcement mesh, an adaptive mesh generation method is used to generate non-standard cross-shaped basic calculation units. The equivalent parameters and stiffness matrix of the thin plate are corrected for the non-standard units through the principle of local stiffness equivalence. Then, the local equivalent results are spliced ​​and integrated to complete the mechanical analysis of the overall irregular steel reinforcement component.

[0075] In practical engineering, irregularly shaped, angled, and non-uniformly meshed steel reinforcement components account for a very high proportion. The standard cross-shaped element in Example 1 is only applicable to regular mesh structures and cannot adapt to the stress characteristics of irregular structures, easily leading to large equivalent deviations and distorted analysis results. This example introduces adaptive mesh generation theory and the principle of local stiffness equivalence correction. It generates non-standard calculation elements for the structural characteristics of irregular steel reinforcement components and matches the actual stress characteristics of the elements through local stiffness correction. While retaining the core logic of the basic method, it expands the applicability of the method.

[0076] The calculation of local stiffness and parameter correction for non-standard elements is as follows:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, The local equivalent stiffness of the non-standard cross element; The equivalent stiffness of a standard cross element; This is the comprehensive correction factor for local stiffness; , This refers to the in-plane shear modulus of the corrected non-standard element. , The out-of-plane rotational modulus of the corrected non-standard element; For non-standard unit reinforcement spacing, The standard unit's reinforcement spacing is used as the reference spacing. The angle of rebar arrangement for non-standard units; This is a correction factor for irregular structures, determined based on the degree of irregularity of the parts.

[0083] This embodiment automatically divides the structural features of irregular steel reinforcement components into suitable non-standard calculation units. By using correction coefficients, the standard unit parameters are transformed into the true equivalent parameters of the non-standard units. Then, the local equivalent results are spliced ​​and integrated into the overall analysis results. The entire process does not change the thin plate equivalence and stiffness calculation logic of the basic method. It can accurately complete the mechanical analysis of irregular, inclined, and non-uniformly arranged steel reinforcement components, covering various complex engineering application scenarios.

[0084] Example 4 To further illustrate with reference to Example 1, in step S1, for complex steel reinforcement components with double or multiple layers, the layered thin plate equivalent method is adopted to convert each layer of steel reinforcement into an independent orthogonal anisotropic thin plate element. In steps S3 to S4, the reduced stiffness matrix, in-plane stiffness matrix and out-of-plane stiffness matrix of each layer of thin plate are calculated respectively. The stiffness matrices of each layer are superimposed and merged to form an overall equivalent model. Then, based on the overall model, step S5 is executed to complete the mechanical response analysis.

[0085] In welded steel reinforcement components with double or multiple layers, each layer of reinforcement is subjected to independent stress and works collaboratively. The single-layer thin plate equivalent in Example 1 cannot reflect the stiffness contribution of each layer of reinforcement, which will lead to an underestimation of the overall stiffness and an overestimation of the deformation prediction. This example adopts the layered thin plate equivalent theory and the principle of stiffness matrix superposition. The multi-layered reinforcement is decomposed into independent thin plate units, and the stiffness is calculated separately. Then, the overall stiffness is obtained by matrix superposition, which accurately restores the collaborative stress characteristics of the multi-layered reinforcement.

[0086] The layered stiffness calculation and superposition are as follows:

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, For the first The reduced stiffness matrix of a thin plate equivalent to a layer of reinforced concrete; For the first Out-of-plane rotational modulus of a thin plate; For the first In-plane shear modulus of a thin plate; , For the first In-plane and out-of-plane stiffness matrices of a thin plate equivalent to a layer of reinforced concrete; For the first The equivalent thickness of a thin plate with multiple layers of reinforcing bars; , The overall in-plane and out-of-plane stiffness matrix of multi-layer reinforced steel components; This refers to the number of reinforcement layers in the steel reinforcement component.

[0092] This embodiment divides multi-layered reinforcing bars into multiple independent thin-plate elements. Each element undergoes equivalence, parameter solving, and stiffness matrix calculation according to the process in Embodiment 1. The overall stiffness of the multi-layered component is then obtained through linear superposition of the stiffness matrices. The subsequent constitutive model construction and load analysis process are completely consistent with the method in Embodiment 1. This method can accurately reflect the stiffness superposition effect of multi-layered reinforcing bars, solves the mechanical analysis problem of complex reinforced steel components, and the calculation results fully match the actual collaborative stress state of multi-layered reinforcing bars. It is applicable to the mechanical performance analysis of various multi-layered welded steel component parts.

[0093] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for analyzing the mechanics of a reinforcing member based on the theory of orthotropic thin plates, characterized by: The method includes: S1. Select the cross-shaped model of the welded steel reinforcement components as the smallest basic calculation unit. Equip this basic calculation unit with the structural size matching principle as an orthogonal anisotropic thin plate element with consistent planar size, and determine the equivalent thickness of the thin plate based on the structural characteristics of the steel reinforcement intersection node. S2. Based on the principle of equivalent structural stiffness, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate are obtained by equivalent conversion of the stress and deformation of the steel reinforcement element and the thin plate element. S3. Substitute the obtained equivalent material mechanical parameters into the classical thin plate theory system to construct the reduced stiffness matrix of the equivalent thin plate. S4. Using the reduced stiffness matrix as the basis for calculation, the equivalent thickness of the thin plate is integrated to derive the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate. S5. Based on the in-plane stiffness matrix and out-of-plane stiffness matrix, construct a generalized force-deformation constitutive model of anisotropic thin plate, apply external loads of the actual working conditions of the steel reinforcement components to the model, complete the overall mechanical response analysis of the steel reinforcement components, and obtain the stress and deformation results.

2. The method for analyzing the mechanical behavior of a reinforcing member based on the theory of orthotropic thin plates according to claim 1, characterized in that: In step S1, when determining the equivalent thickness of the orthogonal anisotropic thin plate unit, the longitudinal and transverse bars at the cross intersection of the reinforcing steel components are used as the calculation benchmark. The diameters of the longitudinal and transverse bars at the intersection are directly added together, and the resulting value is used as the equivalent thickness of the thin plate unit, ensuring that the structural thickness characteristics of the equivalent thin plate are completely matched with those of the original reinforcing steel cross unit.

3. The method according to claim 1, wherein the method is characterized by: In step S2, the equivalent material mechanical parameters of the orthogonal anisotropic thin plate obtained by solving specifically include the in-plane shear modulus, which characterizes the in-plane shear stress characteristics of the thin plate, and the out-of-plane rotation modulus, which characterizes the out-of-plane rotation stress characteristics of the thin plate. The two types of parameters together accurately reflect the true mechanical properties of the semi-rigid weld joints of the reinforcing steel components.

4. The method according to claim 3, wherein the method is characterized by: In step S2, when solving for the equivalent material mechanical parameters, fixed consolidation constraints are applied to the ends of the longitudinal or transverse bars of the basic calculation unit of the steel reinforcement component. In-plane forces and out-of-plane bending moment loads are applied to the unit respectively. The total deformation of the steel reinforcement is decomposed into three components: the bending deformation of the steel reinforcement itself, the rotational deformation of the steel reinforcement relative to the intersection node, and the deformation caused by the bending of the associated steel reinforcement. The actual deformation of the steel reinforcement unit is converted into the equivalent deformation of the thin plate unit through the deformation equivalence principle, and the equivalent material mechanical parameters of the thin plate are calculated in reverse.

5. The mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory according to claim 1, characterized in that: In step S3, when establishing the equivalent thin plate reduced stiffness matrix, the in-plane shear modulus and out-of-plane rotation modulus obtained by the solution are combined with the lateral deformation ratio parameters of the longitudinal and transverse reinforcing bars of the steel reinforcement component under stress. The reduced stiffness matrix is ​​constructed according to the mechanical theory of orthotropic thin plates to realize the unified correlation between the material parameters and stiffness characteristics of the equivalent thin plate.

6. The mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory according to claim 1, characterized in that: In step S4, when calculating the in-plane stiffness matrix and out-of-plane stiffness matrix of the equivalent thin plate, the in-plane stiffness matrix is ​​obtained by multiplying the reduced stiffness matrix with the equivalent thickness of the thin plate, and the out-of-plane stiffness matrix is ​​obtained by proportionally multiplying the reduced stiffness matrix with the cube of the equivalent thickness of the thin plate. The two types of stiffness matrices correspond to the in-plane stress and out-of-plane bending stress characteristics of the steel reinforcement component, respectively.

7. The mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory according to claim 1, characterized in that: In step S5, after completing the mechanical response analysis of the reinforcing steel components, the overall displacement distribution data and internal stress distribution data of the reinforcing steel components under external loads are output. The obtained data can be directly used to guide the hoisting construction, alignment connection and structural alignment control of the reinforcing steel components.

8. The mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory according to claim 1, characterized in that: In step S2, when solving for the equivalent material mechanical parameters, the in-plane rotational stiffness and out-of-plane rotational stiffness of the weld point are dynamically corrected by combining the specifications and dimensions of the longitudinal and transverse reinforcing bars of the steel reinforcement component, the actual welding process parameters, and the weld leg size. Based on the corrected weld point rotational stiffness, the equivalent material mechanical parameters of the thin plate are calculated.

9. The mechanical analysis method for reinforced steel components based on orthotropic thin plate theory according to claim 1, characterized in that: steps In S1, for irregular steel reinforcement components with irregular shapes and non-uniform steel reinforcement mesh, an adaptive mesh generation method is used to generate non-standard cross-shaped basic calculation units. The equivalent parameters and stiffness matrix of the thin plate are corrected for the non-standard units through the principle of local stiffness equivalence. Then, the local equivalent results are spliced ​​and integrated to complete the mechanical analysis of the overall irregular steel reinforcement components.

10. The mechanical analysis method for reinforcing steel components based on orthotropic thin plate theory according to claim 1, characterized in that: In step S1, for complex steel reinforcement components with double or multiple layers, the layered thin plate equivalent method is adopted to convert each layer of steel reinforcement into an independent orthogonal anisotropic thin plate element. In steps S3 to S4, the reduced stiffness matrix, in-plane stiffness matrix and out-of-plane stiffness matrix of each layer of thin plate are calculated respectively. The stiffness matrices of each layer are superimposed and merged to form an overall equivalent model. Then, based on the overall model, step S5 is executed to complete the mechanical response analysis.

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